After reading the book How to solve it by Polya [Pol73], I decided to analyze different ways of problem solving based on how my colleagues and students (altogether 10 volunteers) proved the following simple lemmas: (1) For all prime numbers p≥5 prove that z=p2-1 is divisible by 24 and (2) Proof that the center of gravity of a polygon equals the average of all points of the polygon. Although no representative survey was carried out, the case study brought up some interesting findings: For (1), some person wrote a lot of explanatory text for almost every step of their proof; while others skipped several steps they found obvious. The level of formality varied among the test persons: some wrote their proofs very close to a form that could be verified by e.g. theorem provers, while others stick to a rather informal writing of their proofs. Moreover, the test persons took different approaches of how to proof the lemma: Some could easily write down a formal proof, while others started with examples and counter examples to get a better idea of how to solve the given problem. For (2), some test persons used drawings to get a better idea whether they had to proof or refute the given geometric problem.
Archive for March, 2008
Case Study On Proving Practice
Thursday, March 27th, 2008CodeML competitors (or hopefuls)
Monday, March 24th, 2008I have just stumbled upon another justification (as in people having problems with the currenct state of the art) of our CodeML project: integrating code with syntax highlighting into presentations (and web pages, …), i.e. into situations, where we do not have a suitable parser at hand, but still want to change the appearance of the code, and have access to the semantics and structure.
Submitting content to OMBase and logging
Monday, March 24th, 2008While I was reading up on the REST papers in my last post, I stunbled upon the following best practice for making sure that material is only submitted once to a RESTful application. This is something we should adopt in OMBase as well, just to be safe.
Another thing that we should think of in this arena is to enable some form of RESTful logging facility, so that users can find out what happened to the content. The technology that seems best suited for that seems to be RSS or Atom Syndication (probably the latter). The nice thing is that we could log all the changes to any URI we use in the system. I am not sure under which URL we would address the log, one idea is to just make use of the the mime type application/atom+xml just as for the xhtml presentation as suggested in my last post that would at least alleviate the choice of URL.
Integrating Presentation into OMBase
Monday, March 24th, 2008I have just been reading up on REST again, since I found a very palatable pair of articles (REST intro, and practices). This got me thinking about the state of OMBase, and the integration of our presentation pipeline into the OMBase interface. It is RESTful, since we have MMT addressing via URIs implemented. You just use a GET to retrieve them.
What I have talked with Florian about, but maybe not with the OMBase team, is how to integrate presentation. That should be very simple from the interface point of view: we just take the same URLs, but a different HTTP header.
GET /arith1/lcm
Host: cds.omdoc.org
Accept: application/omdoc+xml
gives you the OMDoc file and
GET /arith1/lcm
Host: cds.omdoc.org
Accept: application/xhtml+xml
gives you the presented version (with the standard options). Now, we have written a paper about presentation and submitted it to MKM and Christine has spent a lot of ingenuity on defining user options to the presentation process.This should be easy to integrate with the URI query interface:
GET /arith1/lcm?ext=foo.ntn∫=lang:ntn;style:physics
Host: cds.omdoc.org
Accept: application/xhtml+xml
That should do the trick.
MathML Support in Firefox 3 beta 4.
Sunday, March 16th, 2008I have just installed the new firefox 3 beta 4. I have been using betas of Firefox3 for a while, and have been enthusiastic about the release, but always had to keep a Firefox 2 copy around for viewing MathML. Without having tested this extensively, I would say that in beta 4, the level of MathML support is up to the level of Firefox 2, which allows me to make the transition to Firefox 3 fully. For some reason I do not fully understand, it seems that the font problems I was having with FF2 have also gone away.
To test FF3, I have looked at our MathML version of the Cornell eprint arXiv and the results are really impressive.